Three Essays on Heterogeneous Large Panel Data Models

This dissertation consists of three papers which contribute to the estimation and inference theory in heterogeneous large panel data models. The first chapter studies a panel threshold model with interactive fixed effects. The least-squares estimators in the shrinking-threshold-effect framework are explored. The inference theory on both slope coefficients and the threshold parameter is derived, and a test for the presence of the threshold effect is proposed. The second chapter considers the least-squares estimation of a panel structure threshold regression (PSTR) model, where parameters may exhibit latent group structures. Under some regularity conditions, the latent group structure can be correctly estimated with probability approaching one. A likelihood-ratio-based test on the group-specific threshold parameters is studied. Two specification tests are proposed: one tests whether the threshold parameters are homogeneous across groups, and the other tests whether the threshold effects are present. The third chapter studies high-dimensional vector autoregressions (VARs) augmented with common factors. An $\ell_{1}$-nuclear-norm regularized estimator is considered. A singular value thresholding procedure is used to determine the correct number of factors with probability approaching one. Both standard and conservative LASSO estimators are employed to improve estimation. The conservative LASSO estimates of the non-zero coefficients are shown to be asymptotically equivalent to the oracle least squares estimates. Monte Carlo studies are conducted to check the finite sample performance of the proposed test and estimators. Empirical applications are conducted in each chapter to illustrate the usefulness of the proposed methods.